Abstract
We consider a new type of mappings in metric spaces which can be characterized as mappings contracting perimeters of triangles. It is shown that such mappings are continuous. The fixed point theorem for such mappings is proved and the classical Banach fixed-point theorem is obtained like a simple corollary. Examples of mappings contracting perimeters of triangles which are not contraction mappings are constructed.
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Acknowledgements
The author is thankful to the anonymous referee for the valuable comments and suggestions that improved the results. The author was partially supported by the Grant EFDS-FL2-08 of The European Federation of Academies of Sciences and Humanities (ALLEA).
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Petrov, E. Fixed point theorem for mappings contracting perimeters of triangles. J. Fixed Point Theory Appl. 25, 74 (2023). https://doi.org/10.1007/s11784-023-01078-4
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DOI: https://doi.org/10.1007/s11784-023-01078-4